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Mensuration: Formulas & Solved Examples - Notes | Study Quantitative Aptitude (Quant) - CAT

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Areas
Volume
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Areas

Areas of some well-known figures are given below:

Mensuration: Formulas & Solved Examples - Notes | Study Quantitative Aptitude (Quant) - CATMensuration: Formulas & Solved Examples - Notes | Study Quantitative Aptitude (Quant) - CATMensuration: Formulas & Solved Examples - Notes | Study Quantitative Aptitude (Quant) - CATMensuration: Formulas & Solved Examples - Notes | Study Quantitative Aptitude (Quant) - CATMensuration: Formulas & Solved Examples - Notes | Study Quantitative Aptitude (Quant) - CAT
Mensuration: Formulas & Solved Examples - Notes | Study Quantitative Aptitude (Quant) - CAT

Mensuration: Formulas & Solved Examples - Notes | Study Quantitative Aptitude (Quant) - CAT 

Example.1 A horizontal pipe for carrying floodwater has a diameter of 1 m. When water in it is 10 cm deep then the width of water surface AB is equal to ________ cm.

Mensuration: Formulas & Solved Examples - Notes | Study Quantitative Aptitude (Quant) - CAT
(1) 10 cm 
(2) 25 cm
(3) 60 cm 
(4) 70 cm
(5) None

Correct Answer is Option (3).

Mensuration: Formulas & Solved Examples - Notes | Study Quantitative Aptitude (Quant) - CAT

  • Let O be the centre of circle.
  • In ΔOAD
    ⇒ 502 = 402 + x2
    ⇒ 2500 – 1600 = x2
    ⇒ x2 = 900
    ⇒ x = 30
  • ∴ AB = 2x = 60 cm. 

Question for Mensuration: Formulas & Solved Examples
Try yourself:The area of quadrilateral PQRS is 228cm2. Find the length of QA.
Mensuration: Formulas & Solved Examples - Notes | Study Quantitative Aptitude (Quant) - CAT
View Solution
 


Example.2 Area of the shaded region is:
Mensuration: Formulas & Solved Examples - Notes | Study Quantitative Aptitude (Quant) - CAT

Mensuration: Formulas & Solved Examples - Notes | Study Quantitative Aptitude (Quant) - CAT

 Correct Answer is Option (1).

Mensuration: Formulas & Solved Examples - Notes | Study Quantitative Aptitude (Quant) - CAT

 

Volume

Mensuration: Formulas & Solved Examples - Notes | Study Quantitative Aptitude (Quant) - CATMensuration: Formulas & Solved Examples - Notes | Study Quantitative Aptitude (Quant) - CATMensuration: Formulas & Solved Examples - Notes | Study Quantitative Aptitude (Quant) - CAT

 

Length of a Diagonal

  • The length of diagonal of a cuboid =  Mensuration: Formulas & Solved Examples - Notes | Study Quantitative Aptitude (Quant) - CAT
  • The length of a diagonal of a cube = Mensuration: Formulas & Solved Examples - Notes | Study Quantitative Aptitude (Quant) - CAT

 

Example.3 An insect is crawling to climb a 20 metre long pipe of diameter 3.5 metres. If the insect take 4 circular rounds to reach the top of the building, then what will be total distance (in nearer metres) traveled by insect to reach the top?
(1) 47 m 
(2) 48 m 
(3) 49 m 
(4) 50 m

  • Since the insect is moving in circular way, so it will cover the distance which will be 4 times the distance of the longest side AB of a right angled triangle. In the figure AO is equal to the circumference of the pipe.
    AO = πd = Mensuration: Formulas & Solved Examples - Notes | Study Quantitative Aptitude (Quant) - CAT  = 11m
    BO = 5 m
    AB = Mensuration: Formulas & Solved Examples - Notes | Study Quantitative Aptitude (Quant) - CAT = Mensuration: Formulas & Solved Examples - Notes | Study Quantitative Aptitude (Quant) - CAT = 12.08 m
  • Total distance traveled = 12.08 × 4 = 48.32 m
  • Hence distance in nearer meters = 48 m
    Mensuration: Formulas & Solved Examples - Notes | Study Quantitative Aptitude (Quant) - CAT

Question for Mensuration: Formulas & Solved Examples
Try yourself:What is the volume of a cone having radius of 21cm and height of 5cm?
View Solution

 

Example.4 The surface area of a cube is 726 sq metres. Find the volume of the cube
(1) 1234 m2 
(2) 1431 m2
(3) 1341 m3 
(4) 1331 m3 
(5) None of these

Correct Answer is Option(4).

  • Surface area S = 726 m2 Volume V = ?
  • In a cube,
  • S = 6a2 = 726 ⇒ a2 = 121 ⇒ a = 11 m
  • So, V = a3 = 113 = 1331 m3.
The document Mensuration: Formulas & Solved Examples - Notes | Study Quantitative Aptitude (Quant) - CAT is a part of the CAT Course Quantitative Aptitude (Quant).
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